Differentiable function and the graph of derivative

Question

Solve the below:

1. Find f(x), given that f'(x)=20x+3cos(x)

for all x and f(0)=2

2. Given that f is a differentiable function and the graph of its derivative is shown below, find the interval(s) in which f is decreasing.

3. Find the critical numbers and the local extreme values of

f(x)=5x³/3+10x+1

a) Critical numbers are -2 and 2. Local Maximum at -2 and Local Minimum at 2.

b) No critical numbers and no local extrema.

c) Critical numbers are 2 and 0. Local Maximum at 2 and Local Minimum at 0.

d) Critical numbers are -2 and 0. Local Maximum at -2 and Local Minimum at 0.

e) Critical numbers are -2 and 2. Local Maximum at -2 and Local Minimum at 0.

4. Find the the local extreme values of

f(x)=2x²- 4/x⁴

a) Local Max: f(0) = 125, f(5) = 125; Local Min: f(-5) = 25

b) No local extrema.

c) Local Max: f(-5) = 125, f(5) = 125; Local Min: f(0) = 25

d) Local Max: f(-5) = 125; No Local Min

e) Local Max: f(-5) = 125; Local Min: f(0) = 25, f(5) = 25

f) None of the above.

5. Find the critical numbers of f(x)=2-5x/2+5x

a)No critical numbers.

b) -2/5, 0 and 2/5

c) -2/5 and 0

d) -2/5, 0 and 5

e) -5 and 5